The "BASICS" or "Building Accuracy and Speed In Core
Skills" Mathematics Intervention Program has been designed to
enable students who are either low-achievers or have some form of
learning disability, to attain real improvement and make the successful
transition to core mathematics. The literature was reviewed to identify
a collection of specific needs and deficiencies that these groups of
students have historically exhibited in the mathematics classroom.
Common issues identified through the review of the literature included
the; use of inefficient and/or error-prone approaches; time-consuming
mental computations; and a focus on simple mundane tasks in lieu of
higher-order cognitive tasks (Bezuk & Cegelka, 1995; Pegg &
Graham, 2007). The BASIC Intervention Program was designed to address
these issues through a significant focus on improving the automaticity
and accuracy of the recall of basic mathematical facts, rules, concepts
and procedures. By improving automaticity and accuracy, we are negating
the greatest impediments to increasing these students' opportunity
for success. Consequently, the purpose of the program is to reverse the
cycle of continual low-academic performance for these students, at the
same time, equipping them with the essential tools to gain success and
achieve their potential in mathematics now and into the future. The
ultimate aim is to increase the likelihood that these students can
attain success in secondary mathematics, which will facilitate a more
successful transition to post-school life. The structure of this
program, its pedagogical strategies and assessment devices has been
significantly influenced by the QuickSmart Program developed at the
SiMERR National Centre at the University of New England.

Theoretical framework

The focus on both the accuracy and speed of recall of basic
mathematical skills and concepts is designed to rectify the influential
roadblocks to higher-order thinking, which are related to cognitive
capacity and time (Graham, Pegg, Bellert & Thomas; Pegg &
Graham, 2007). To start with, all students have a limited cognitive
capacity, which means the amount of information that can be processed by
their working memory is limited (Pegg & Graham, 2007). If a
student's information retrieval skills and /or processing speed of
sub-tasks are inefficient, their working memory reaches its cognitive
limit. Consequently, this restricts their ability to progress through
the task (Pegg & Graham, 2007). By increasing automaticity the time
taken for a student to perform subtasks is decreased, which frees up
their working memory. This enables students to move through the task
with greater efficiency, ultimately reach a solution quicker and with
more time and cognitive resources available to tackle higher-order tasks
(Graham et al., 2004).

At-risk students

Students with learning disabilities or those with a history of
low-achievement are the target group of this intervention project.
Low-achieving students are typically students who: consistently achieve
significantly low performance on standardised tests; perform poorly in
in-class summative assessment; are placed in remedial mathematics
classes; and have no formally assessed learning disability (Baker,
Gersten & Lee, 2002). On the other hand, students who are classed as
having a "learning disability" are derived from three broad
categories, namely those students with: identifiable disabilities and
impairments; learning difficulties not attributed to disabilities or
impairments; and difficulties due to socio-economic, cultural, or
linguistic disadvantage (Westwood, 2003). For the purpose of this
project, when dealing with aspects directly related to both groups of
students, they will be referred to as "at-risk students."

At-risk students who have difficulties in mathematics tend to use
time-consuming, inefficient, and/or error prone strategies to solve
simple calculations. In contrast, average-achieving students recall
basic elements quickly and accurately (Pegg & Graham, 2007). At-risk
students spend a greater proportion of the time on low-level tasks, to
the detriment of the mathematical competence and the opportunity to
engage in higher-order cognitive processes (Pegg & Graham, 2007).
Consequently, the support mechanisms for at-risk students must provide
them with the ability to reduce their cognitive processing load related
to basic skills, through focused practice, continual reinforcement and
the development of efficient strategies.

The aims

The short-term aims of the "Basics" Intervention Program
are to improve the accuracy and recall of information retrieval time of
simple mathematics concepts and skills for at-risk students. Pegg and
Graham (2007) identify that an intervention program focused on improving
the automaticity and accuracy of basic mathematical skills and concepts
enables students to shift their focus from coping with mundane or
routine tasks to engaging in higher-order mental processes. The longer
term aims of this program are to enable at-risk students to engage in
higher-order cognitive tasks with greater efficiency and success.
Ultimately, at-risk students who participate in this program will have a
greater chance of making a successful transition to core mathematics
will break free of the perception "that they cannot do
mathematics" and will be better equipped for post-school life.

Proposed model

The proposed model is based on a balance of strategies comprising:
explicit teaching; specific questioning sequences; direct modelling of
problem-solving skills; structured and guided problem-solving tasks; and
diagnostic and formative task elements to assess understanding of
targeted student learning. The model is designed also to cover the
elements of the respective year level's work program. The model
follows a pyramid structure (Figure 1), which emphasis three distinctive
but sequential "levels" of instruction where each level is
built upon the solid foundation of the previous level. The diagnostic
and formative task elements are continuous and facilitated through the
relevant year level section of the Blackboard learning management
system. The pyramid structure is designed to give a representation of
the proportion of time that each level should be allocated during each
unit. The subsections that follow give a more detailed perspective, aims
and teaching strategies of this proposed model.

This level encompasses the use of considerable direct instruction
to develop meaningful retention, recall and automaticity of basic
mathematics rules skills and concepts. The aim is for students to master
basic rules, skills and concepts to develop a solid mathematical
foundation and to free up their working memory for higher cognitive
activities encompassed in Level 2 and 3 (Jones & Southern, 2003;
McNamara & Scott, 2001). Teachers focus on utilising deliberate
practice to model and consolidate rules, skills and concepts and provide
support through effective feedback (Jones & Southern, 2003; Minskoff
& Allsopp, 2003). Students must be able to retain learning and to
recall stored knowledge if they are to apply concepts and skills, and
acquire new ones (Bezuk & Cegelka, 1995). Consequently, teachers
must continuously review previously covered material to increase
retention and recall either at the start or conclusion of the class
through short and concise maths maintenance activities (Minskoff &
Allsopp, 2003).

Level 2: Developing problem-solving skills and strategies

The next level focuses the use of direct instruction and mnemonics
to teach problem-solving skills (Greene, 1999). The success of
students' problem-solving efforts is determined by the manner in
which they approach mathematical problems (Bezuk & Cegelka, 1995).
The aim is to develop a small collection of important problem-solving
strategies, such as identifying the known and unknown information and
the relationship between them; identification of the processes and steps
required; and translating information into the right algorithm
(Westwood, 2003). Also the aim is to instruct the students how to
develop a plan to attack a problem and what procedures they need to use
and when (Mercer, 1997). Critical elements for at-risk student success
in problem-solving is the need for them to systematically identify the
required procedures in order to improve their skills in selecting
problem-solving strategies, and increase their efficiency in accurately
implementing the relevant strategies and procedures (Bezuk &
Cegelka, 1995).

Level 3: Hands-on inquiry- based learning in small groups

The final level is a culmination of the previous two and is built
upon its foundation. The aim is to utilise hands-on structured and
inquiry-based learning in small groups to enable students to connect and
consolidate their newly acquired knowledge, to their existing conceptual
framework and to apply their knowledge to authentic contexts (Anderson
et al, 2004). Inquiry-based learning also provides at-risk students with
the opportunity to learn how to make decisions and judgements among
alternatives and improve their ability to hypothesise and infer (Bezuk
& Cegelka, 1995). The role of the teacher is to monitor the group
work and provide feedback and correct and challenge student responses.
Structured inquiry should be implemented first. Structured inquiry is
when the teacher directs students throughout the inquiry by giving them
the problem, the procedures, and required materials, to enable them to
formulate a pre-determined conclusion (Anderson et al, 2004). The
rationale behind starting with structured inquiry is that it explicitly
teaches students the necessary framework, procedures and possible
strategies for solving a problem (Bezuk & Cegelka, 1995). The next
stage is guided inquiry. This involves the teacher providing the
necessary materials and problem statement to be investigated (Anderson
et al, 2004). Students are asked to generate their own procedure in
solving the problem.

Continuous diagnostic and formative assessment

A key element of this program is the use of continuous diagnostic
and formative assessment. The continuous diagnostic and formative
assessment elements will be designed and hierarchically organised along
a continuum for each topic, to continually reinforce previous skills and
concepts. The assessment and instruction will form a continuous cycle,
as the assessment coupled with teacher observations will provide the
basis of instructional design, delivery and individualisation.

The purpose of this assessment is to continually monitor both
student accuracy and speed of recall as a means of increased
automaticity, during the initial levels of the instruction model (Pegg
& Graham, 2007). Student performance will be monitored through an
individual "Performance Tracker". The aim of the Performance
Tracker is for students to visually monitor a number of key facets of
their progress through various graphical representations, in relation to
a set of student-determined goals (Anderson, 2007; Martin, 2003). The
rationale behind the use of these trackers is to enhance students'
motivation and engagement in mathematics to ultimately assist in
improving self-esteem and reinforce students' beliefs that they
"can do" and achieve success in mathematics (Anderson, 2007;
Martin, 2003).

Program components

The following is a brief outline and description of the key
components of the "Basics" Intervention Program. The key
components of the programs are:

* Pre-testing is utilised to identify what each student already
knows and the specific gaps that exist within their prior knowledge and
understanding. The information from pre-testing is used to tailor
instruction and to address these gaps in each student's prior
knowledge and understanding.

* The results of the pre-testing process are directly linked to the
goal-setting of each student's "Performance Tracker" for
that particular unit.

* The consistent use of timed formative assessment activities aimed
at increasing the speed and proficiency of basic mathematical skills and
concepts.

* The use of interactive learning objects, including online
stopwatches and timers to assist students to 'externalise
time' when completing in-class activities. These timers are used in
conjunction with activities that utilise manipulative materials, flash
cards, concrete objects and interactive pictures or diagrams (including
Java Applets).

* Simple games and warm-up activities including Quick Reviews,
Dominos, Bingo, Three in a Row, Same Sums Fast Facts.

* Small group work on simple problem-solving tasks.

Initial results

The first six months of the BASICS trial has been extremely
successful, with the comments from participating teachers being very
positive. The enthusiasm and professionalism of the teachers involved in
the trial as been instrumental to its success, which is indicated by
three key performance indicators. The first is the increased number of
students making the transition from the trial classes to the core
mathematics program. At this stage, nearly one quarter of the students,
who began the year in one of the three participating classes, have made
a successful transition to the core mathematics program. This is a
significant increase in the movement of students to the core program
compared to the same time last year. It is envisaged in the next three
month period at least another ten students, based on their improved
academic outcomes and self-belief, will move to core program. The second
key performance indicator is the substantial increase in class averages,
as compared to the previous year's data. In all three trial
classes, the average has increased by at least 15% and is detailed in
Table 1. The final performance indicator is the decrease in the number
of students who failed to reach a satisfactory standard. At the same
time last year thirty three students failed to reach a satisfactory
standard. During the trial, this number has decreased by one-third, with
only eleven students failing to reach a satisfactory standard. It should
be noted, that the trial classes have completed the same assessment
tasks as the core classes, with only slight modifications on the basis
of special consideration.

Conclusion

The "BASICS" Intervention Program is novel in its balance
and integration of the optimal aspects of instruction from direct,
constructivist and contextually-based instruction designed to meet the
specific needs of at-risk students. The specific focus of this program
is to address the memory and recall difficulties and inability to
approach, structure and solve problem-solving tasks experienced by
at-risk students. In addition, the use of continuous diagnostic and
formative assessment will enable both teachers and students to develop
positive relationships and improve student self-concept. The
program's basis on a strong theoretical framework and excellent
teacher uptake has produced significant improvement in student
achievement and attitude to mathematics in all three trial classes.
These results indicate that when provided with the right environment,
at-risk students can achieve real success on work that is at comparable
level of work undertaken in a core mathematics program.